On hierarchical joint source-channel coding with degraded side information

We extend the setting of two-stage lossy source coding with successive refinement structures into a joint source-channel coding setting. In particular, we consider a problem where two descriptions of a memoryless source are to be transmitted across two independent memoryless channels and where the o...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 52; no. 3; pp. 886 - 903
Main Authors: Steinberg, Y., Merhav, N.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.03.2006
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Applied sciences
Channel coding
Channels
Coding
Coding, codes
Data processing
Decoders
Decoding
Degradation
Descriptions
Distortion measurement
Encoders
Exact sciences and technology
Feedback
Hierarchical coding
Information technology
Information, signal and communications theory
joint source-channel coding
Markov analysis
Memoryless systems
Optimization
Output feedback
Performance loss
side information (SI)
Signal and communications theory
Source coding
Statistical distributions
successive refinement
Sufficient conditions
systematic coding
Telecommunications and information theory
Theorems
Wyner-Ziv problem
Performance evaluation
Block code
joint source-channel coding
Multistage method
Source coding
successive refinement
Necessary and sufficient condition
Refinement method
Two channel system
Lossy medium
Joint source channel coding
side information (SI)
Implementation
Markov chain
Memoryless channel
systematic coding
Wyner-Ziv problem
Wyner Ziv problem
Hierarchical coding
Memoryless source
ISSN:0018-9448, 1557-9654
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Summary:We extend the setting of two-stage lossy source coding with successive refinement structures into a joint source-channel coding setting. In particular, we consider a problem where two descriptions of a memoryless source are to be transmitted across two independent memoryless channels and where the output of the channel corresponding to the first (coarse) description is also available to the decoder of the second (refinement) decoder. Side information (SI), correlated to the source, may also be available to the decoders. In such a case, we confine attention to degraded SI, in the sense that the source, the SI available at the refinement decoder, and the SI available at the coarse decoder form a Markov chain in this order. Our first result is a separation theorem asserting that in the limit of long blocks, no optimality is lost by first applying lossy successive-refinement source coding, regardless of the channels, and then applying good channel codes to each one of the resulting bitstreams, regardless of the source and the SI. It is also shown that (even noiseless) feedback from the output of the first channel to the input of the second encoder cannot improve performance, but may sometimes significantly facilitate the implementation of optimum codes. We provide two examples where single-letter codes (of unit block length) achieve optimum performance, if feedback from the channel output of the first stage is provided to the encoder of the refinement stage. In one of these examples, it is evident that if feedback is not provided, optimality cannot be achieved with unit length code. Motivated by these examples, we then investigate single-letter codes for this system. Necessary and sufficient conditions are furnished for the optimality of single-letter codes with and without feedback. A corollary of these conditions is that for the quadratic distortion measure, feedback is necessary to achieve optimality in single-letter codes, regardless of the source distribution and the channel statistics
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2005.864423